Deforming a plane over a topology
Destructive workflow (easy but requires joining meshes)


first put another plane, the same size as your probe plane, just below the two objects, to represent the zero level
Join all the "target" meshes (including the "zero" plane, excluding the probe plane) in a single object, by selecting all of them and hitting CtrlJ
Subdivide your probe plane as much as the resolution you require


On your probe plane, add a Shrinkwrap Modifier. Use your target mesh as "target", and the options: "Project", "On surface", Axis: "Z", both "Negative" and "Positive"


In the viewport you will see an overlap between your probe and your target (which is what you wanted! but it looks weird). So I applied the modifier (Apply) and moved the probe a bit up, and used X-Ray for visualisation purposes:

 


Add: with a Catmull-Clark Subsurface Modifier and a purpose-made shader:



or you could even duplicate the object (without subdivision surface!), and on the duplicate use a black material and a Wireframe modifier to make it look more like a plot:



Non-destructive workflow

You will need: 


a zero-level plane, with one "Boolean" modifier of type "Union" for each object in your scene. This way, you will be able to modify the objects separately, while their changes will be reflected real-time on the "zero-level" plane
your target plane, with 


Shrinkwrap set as in the workflow above, using the "zero-level" plane as a target
A Displace modifier without texture, acting only along the Z axis
A shader like the one above



This is the result:



And the file (requires Blender 2.8 and may not be compatible with post-Alpha versions):